In today's society, many devices include a controller that generates a control signal that controls movement and/or operation of another component of a device. One example of such a device is a hard disk drive (HDD). In a typical HDD, data is stored on a circular disk. Heads for reading and writing are located on an arm that is positioned over the disk. A track servo system moves the arm over the disk to position the heads over a particular portion of the disk for reading and/or writing of data from/to that portion of the disk as the disk is rotated by a motor. A controller generates control signals that are transmitted to the servo system to position the arm over the disk to read and/or write desired data.
As technology has advanced, HDDs have become smaller and smaller and included in more devices. As the HDDs have become smaller, it is a problem that the servo systems in HDDs are required to hold read/write heads to very small off-track errors to support the increasing track density of disks. Tracking errors can be induced due to many effects including disk and bearing run-out; servo-track-writer induced irregularities; electronic noise; spindle and actuator resonances; and external shock and vibration excitations. The tracking errors cause noise in the control signal applied to the servo system by the controller. The controller monitors the signal applied to the plant to correct the signal to account for the noise added by these tracking errors.
Typically, the tracking errors induced by disk and bearing run-out; servo-track-writer induced irregularities; electronic noise; and spindle and actuator resonances cause high frequency noise in the control signal. Thus, the controller must adjust the control signal to remove this noise.
It is well know to use carefully designed notch filters to attenuate mechanical resonances, such as the spindle and actuator resonances. In order to attenuate the mechanical resonance the notch filter must have center frequencies that follow the shift frequency of the mechanical resonance. However, designing such a notch filter is difficult due to the variation in resonance frequencies in individual drives caused by variations of mechanical components and the manufacturing process. Alternatively, the notch filter may be designed to have a wide range of attenuation. However, the wide range of attenuation leads to phase loss in the signal. Another problem with the use of notch filters is that mechanical resonances often have multiple resonant modes. Thus, multiple notch filters are needed to filter out the multiple modes. The use of multiple notch filters significantly affects the stability margins of the signal, makes design of the filters more complicated and requires more code space to implement the multiple filters.
To overcome the problems with the use of notch filters to attenuate mechanical resonances, U.S. Pat. No. 6,710,965 titled “Phased-Advanced Filter for Robust Resonance Cancellation” in the name of Ding et al. issued 23 Mar. 2004 discloses the use a phase-advanced low pass filter to attenuate mechanical resonances. The proposed filter is a low pass filter with a transfer function that includes either (z+1) in the numerator of the transfer function. By replacing (z+1) with 2z in the numerator of the filter causes the phase of the filter to advance by wTs/2, where Ts is the sampling period. However, the amplitude of 2z is much larger than the amplitude of (1+z). Thus, the magnitude of the phase-advanced filter will be amplified at a high frequency range. Thus, there is a need in the art for a low pass filter that can significantly attenuate multiple mechanical resonances from a control signal that is not unacceptably amplified at a high frequency range.